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  "kaggle": {
   "accelerator": "nvidiaTeslaT4",
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   "id": "772f1079d76766c9",
   "cell_type": "code",
   "source": [
    "import torch\n",
    "from collections import OrderedDict\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "#from pyDOE import lhs#拉丁超立方抽样\n",
    "from torch import nn\n",
    "import time\n",
    "import warnings\n",
    "from torch.optim.lr_scheduler import StepLR\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)  # 只忽略UserWarning类型的警告"
   ],
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   "outputs": [],
   "execution_count": 101
  },
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   "cell_type": "code",
   "source": [
    "if torch.cuda.is_available():\n",
    "    device = torch.device('cuda')\n",
    "else:\n",
    "    device = torch.device('cpu')\n",
    "def setup_seed(seed):\n",
    "    torch.manual_seed(seed)\n",
    "    torch.cuda.manual_seed_all(seed)\n",
    "    np.random.seed(seed)\n",
    "    #  random.seed(seed)\n",
    "    torch.backends.cudnn.deterministic = True\n",
    "\n",
    "setup_seed(124)\n",
    "dtype = torch.double"
   ],
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   "outputs": [],
   "execution_count": 102
  },
  {
   "id": "fe0818329fdb65c3",
   "cell_type": "code",
   "source": [
    "#求导\n",
    "def gradients(outputs, inputs):\n",
    "    return torch.autograd.grad(outputs, inputs, grad_outputs=torch.ones_like(outputs), create_graph=True)\n",
    "#类型转换\n",
    "def to_numpy(input):\n",
    "    if isinstance(input, torch.Tensor):\n",
    "        return input.detach().cpu().numpy()\n",
    "    elif isinstance(input, np.ndarray):\n",
    "        return input"
   ],
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   "outputs": [],
   "execution_count": 103
  },
  {
   "id": "60a72b4d3732df3b",
   "cell_type": "code",
   "source": [
    "#构建网络layers\n",
    "def Dnnlayers(input_layers,output_layers,hidden_layers,neural):\n",
    "    layers = []\n",
    "    for i in range(hidden_layers + 2):\n",
    "        if i == 0:\n",
    "            layers.append(input_layers)\n",
    "        elif i == hidden_layers + 1:\n",
    "            layers.append(output_layers)\n",
    "        else:\n",
    "            layers.append(neural)\n",
    "    return layers"
   ],
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   "outputs": [],
   "execution_count": 104
  },
  {
   "id": "4c739aded6291406",
   "cell_type": "code",
   "source": [
    "class DNN(nn.Module):#for u and f\n",
    "    def __init__(self, layers):\n",
    "        #继承父类\n",
    "        super(DNN, self).__init__()\n",
    "\n",
    "        #depth of network\n",
    "        self.depth = len(layers) - 1\n",
    "        #print(self.depth)\n",
    "\n",
    "        #activation of network\n",
    "        self.activation = nn.Tanh()\n",
    "        self.positive_activation = nn.Softplus()\n",
    "        #create the neural network\n",
    "        layers_list = list()\n",
    "        for i in range(self.depth - 1):\n",
    "            layers_list.append(\n",
    "                ('layer_%d' % i, nn.Linear(layers[i], layers[i+1]))#create each network\n",
    "            )\n",
    "            layers_list.append(\n",
    "                ('activation_%d' % i, self.activation)  #create each activation of network\n",
    "            )\n",
    "        layers_list.append(\n",
    "            ('layer_%d' % (self.depth - 1), nn.Linear(layers[-2], layers[-1]))\n",
    "            #last network do not have activation\n",
    "        )\n",
    "        #创建一个有序字典，其中包含了从 layers_list 中获得的键值对，这在需要保持元素顺序的场景（如神经网络层的顺序）中非常有用。\n",
    "        layerDict = OrderedDict(layers_list)\n",
    "\n",
    "        #deploy layers\n",
    "        self.layers = nn.Sequential(layerDict)\n",
    "        #print(self.layers)\n",
    "        self.positive_activation = nn.Softplus()  # 定义 Softplus 激活函数\n",
    "    #forword network,output the result of network\n",
    "    def forward(self, x):\n",
    "        #out = torch.exp(self.layers(x))\n",
    "        out = self.layers(x)\n",
    "        #out = self.positive_activation(out)  # 这里使用 Softplu#ln(e^x+1)\n",
    "        #out = self.positive_activation(out)\n",
    "        return out"
   ],
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   "outputs": [],
   "execution_count": 105
  },
  {
   "id": "d07f63b4c7b9d6b7",
   "cell_type": "code",
   "source": [
    "class Net_2_for_f():\n",
    "    def __init__(self, layers):\n",
    "        self.dnn = DNN(layers).double().to(device)\n",
    "    def l2_loss(self):\n",
    "        l2_loss = torch.tensor(0.0, device=device, dtype=dtype, requires_grad=True)\n",
    "        for name,parma in self.dnn.named_parameters():\n",
    "            if 'bias' not in name:\n",
    "                l2_loss = l2_loss + (0.5 * torch.sum(torch.pow(parma,2)))\n",
    "        return l2_loss\n",
    "    def loss_pde(self, u, u_t):\n",
    "        f = self.dnn.forward(u)\n",
    "        f = ((u_t+f)**2).mean()\n",
    "        return f\n",
    "#\n"
   ],
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   "outputs": [],
   "execution_count": 106
  },
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   "cell_type": "code",
   "source": [
    "data = scipy.io.loadmat(r'c_two_none_f_predict.mat')  # Import Solution data\n",
    "u1 = np.real(data['u'])\n",
    "u_t1 = np.real(data['u_t'])\n",
    "data = scipy.io.loadmat(r'c_one_none_f_predict.mat')  # Import Solution data\n",
    "u2 = np.real(data['u'])\n",
    "u_t2 = np.real(data['u_t'])\n",
    "data = scipy.io.loadmat(r'c_0.5_none_f_predict.mat')\n",
    "u3 = np.real(data['u'])\n",
    "u_t3 = np.real(data['u_t'])\n",
    "\n",
    "u = np.concatenate((u1,u2,u3),axis=0)\n",
    "u_t = np.concatenate((u_t1,u_t2,u_t3),axis=0)\n",
    "#\n",
    "u_train = torch.tensor(u, dtype=dtype, device=device, requires_grad=True)\n",
    "u_t_train = torch.tensor(u_t, dtype=dtype, device=device)"
   ],
   "id": "e335e1aa3a20a60d",
   "outputs": [],
   "execution_count": 107
  },
  {
   "id": "9f67a2ebd1efcaa8",
   "cell_type": "code",
   "source": [
    "#training\n",
    "def train(epoch):\n",
    "    model.dnn.train()\n",
    "    def closure():\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "\n",
    "        loss_pde = model.loss_pde(u_train, u_t_train)\n",
    "        loss_l2 = model.l2_loss()\n",
    "        #total loss\n",
    "        loss =  loss_pde  + alpha * loss_l2\n",
    "\n",
    "        if epoch%10 ==0 :\n",
    "            print(f'epoch:{epoch}, loss:{loss:.8f},loss_pde:{loss_pde:.8f},loss_l2:{loss_l2:.8f}')\n",
    "\n",
    "\n",
    "\n",
    "        loss_total_history.append(to_numpy(loss))\n",
    "        loss_pde_history.append(to_numpy(loss_pde))\n",
    "\n",
    "        loss.backward()\n",
    "        return loss\n",
    "    loss = optimizer.step(closure)"
   ],
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  },
  {
   "id": "24bea047f2118673",
   "cell_type": "code",
   "source": [
    "'''#loss_data(self, x_u, u_data, x_f, f_data):初始 末尾值\n",
    "t_u_train = np.linspace(0.0, 3, 31).reshape(-1, 1)\n",
    "u_data = 1.0/(t_u_train+1.0)\n",
    "#loss_ic(self, x_ic, u_ic, f_ic):\n",
    "t_ic_train = np.linspace(0.0, 0.0, 1).reshape(-1, 1)\n",
    "u_ic = 1.0/(t_ic_train+1.0)\n",
    "f_ic = u_ic**2\n",
    "#loss_pde(self, x_int)\n",
    "t_int_train = np.linspace(0.0, 3, 301).reshape(-1, 1)\n",
    "\n",
    "#tensor化\n",
    "t_u_train = torch.tensor(t_u_train, dtype=dtype, device=device, requires_grad=True)\n",
    "u_data = torch.tensor(u_data, dtype=dtype, device=device)\n",
    "t_ic_train = torch.tensor(t_ic_train, dtype=dtype, device=device, requires_grad=True)\n",
    "u_ic = torch.tensor(u_ic, dtype=dtype, device=device)\n",
    "f_ic = torch.tensor(f_ic, dtype=dtype, device=device)\n",
    "t_int_train = torch.tensor(t_int_train, dtype=dtype, device=device, requires_grad=True)'''"
   ],
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    {
     "data": {
      "text/plain": [
       "'#loss_data(self, x_u, u_data, x_f, f_data):初始 末尾值\\nt_u_train = np.linspace(0.0, 3, 31).reshape(-1, 1)\\nu_data = 1.0/(t_u_train+1.0)\\n#loss_ic(self, x_ic, u_ic, f_ic):\\nt_ic_train = np.linspace(0.0, 0.0, 1).reshape(-1, 1)\\nu_ic = 1.0/(t_ic_train+1.0)\\nf_ic = u_ic**2\\n#loss_pde(self, x_int)\\nt_int_train = np.linspace(0.0, 3, 301).reshape(-1, 1)\\n\\n#tensor化\\nt_u_train = torch.tensor(t_u_train, dtype=dtype, device=device, requires_grad=True)\\nu_data = torch.tensor(u_data, dtype=dtype, device=device)\\nt_ic_train = torch.tensor(t_ic_train, dtype=dtype, device=device, requires_grad=True)\\nu_ic = torch.tensor(u_ic, dtype=dtype, device=device)\\nf_ic = torch.tensor(f_ic, dtype=dtype, device=device)\\nt_int_train = torch.tensor(t_int_train, dtype=dtype, device=device, requires_grad=True)'"
      ]
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     "metadata": {},
     "output_type": "execute_result"
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   ],
   "execution_count": 109
  },
  {
   "id": "24612c77b3401f6c",
   "cell_type": "code",
   "source": [
    "layers = Dnnlayers(1, 1, 3, 15)\n",
    "model = Net_2_for_f(layers)"
   ],
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   "execution_count": 110
  },
  {
   "id": "36fa46ed331a8794",
   "cell_type": "code",
   "source": [
    "loss_total_history = []\n",
    "loss_pde_history = []\n",
    "lr = 0.001\n",
    "alpha = 0.00001\n",
    "optimizer = torch.optim.Adam(model.dnn.parameters(), lr=lr)#,weight_decay=0.0001\n",
    "epochs1 = 15000\n",
    "tic = time.time()\n",
    "for epoch in range(1, epochs1+1):\n",
    "    train(epoch)\n",
    "toc = time.time()"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:10, loss:0.09589666,loss_pde:0.09581854,loss_l2:7.81207608\n",
      "epoch:20, loss:0.03553364,loss_pde:0.03545474,loss_l2:7.89034009\n",
      "epoch:30, loss:0.01211728,loss_pde:0.01203714,loss_l2:8.01401856\n",
      "epoch:40, loss:0.01113539,loss_pde:0.01105419,loss_l2:8.11909577\n",
      "epoch:50, loss:0.00895483,loss_pde:0.00887320,loss_l2:8.16246209\n",
      "epoch:60, loss:0.00626646,loss_pde:0.00618448,loss_l2:8.19867590\n",
      "epoch:70, loss:0.00484704,loss_pde:0.00476426,loss_l2:8.27872673\n",
      "epoch:80, loss:0.00328003,loss_pde:0.00319612,loss_l2:8.39126137\n",
      "epoch:90, loss:0.00213458,loss_pde:0.00204955,loss_l2:8.50275580\n",
      "epoch:100, loss:0.00130373,loss_pde:0.00121774,loss_l2:8.59869752\n",
      "epoch:110, loss:0.00083734,loss_pde:0.00075049,loss_l2:8.68500209\n",
      "epoch:120, loss:0.00062401,loss_pde:0.00053644,loss_l2:8.75699165\n",
      "epoch:130, loss:0.00055788,loss_pde:0.00046983,loss_l2:8.80513577\n",
      "epoch:140, loss:0.00054529,loss_pde:0.00045696,loss_l2:8.83343087\n",
      "epoch:150, loss:0.00054201,loss_pde:0.00045352,loss_l2:8.84868140\n",
      "epoch:160, loss:0.00053760,loss_pde:0.00044905,loss_l2:8.85551479\n",
      "epoch:170, loss:0.00053241,loss_pde:0.00044381,loss_l2:8.85964778\n",
      "epoch:180, loss:0.00052739,loss_pde:0.00043875,loss_l2:8.86409894\n",
      "epoch:190, loss:0.00052257,loss_pde:0.00043388,loss_l2:8.86968515\n",
      "epoch:200, loss:0.00051777,loss_pde:0.00042900,loss_l2:8.87670186\n",
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      "epoch:14940, loss:0.00004571,loss_pde:0.00000255,loss_l2:4.31619273\n",
      "epoch:14950, loss:0.00004568,loss_pde:0.00000253,loss_l2:4.31556976\n",
      "epoch:14960, loss:0.00004568,loss_pde:0.00000253,loss_l2:4.31485795\n",
      "epoch:14970, loss:0.00004567,loss_pde:0.00000253,loss_l2:4.31423342\n",
      "epoch:14980, loss:0.00004567,loss_pde:0.00000253,loss_l2:4.31357422\n",
      "epoch:14990, loss:0.00004566,loss_pde:0.00000253,loss_l2:4.31295491\n",
      "epoch:15000, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31232787\n"
     ]
    }
   ],
   "execution_count": 111
  },
  {
   "id": "86c0f9a889329a74",
   "cell_type": "code",
   "source": [
    "optimizer = torch.optim.LBFGS(model.dnn.parameters(),lr=1.0,max_iter=20)\n",
    "epochs2 = 2000\n",
    "tic = time.time()\n",
    "for epoch in range(1, epochs2+1):\n",
    "    train(epoch)\n",
    "toc = time.time()"
   ],
   "metadata": {
    "id": "86c0f9a889329a74",
    "trusted": true,
    "execution": {
     "iopub.status.busy": "2025-01-08T12:48:27.065211Z",
     "iopub.execute_input": "2025-01-08T12:48:27.065590Z",
     "iopub.status.idle": "2025-01-08T13:16:03.958133Z",
     "shell.execute_reply.started": "2025-01-08T12:48:27.065552Z",
     "shell.execute_reply": "2025-01-08T13:16:03.957165Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "outputId": "1d47db29-97f3-4ce6-f35c-0058712519a9",
    "ExecuteTime": {
     "end_time": "2025-02-28T14:20:24.941491Z",
     "start_time": "2025-02-28T14:20:22.855888Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "epoch:1210, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1220, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1230, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1240, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1250, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1270, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1280, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1290, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1300, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1400, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1420, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1480, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1490, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1500, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1510, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1520, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1540, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1550, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1590, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1600, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1610, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1620, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1630, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1640, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1650, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1660, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1670, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1680, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1690, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1700, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
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      "epoch:1730, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1740, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1750, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1760, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1770, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1780, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1790, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1800, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1810, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1820, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1830, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1840, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1850, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1860, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1870, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1880, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1890, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1900, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1910, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1920, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1930, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1940, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1950, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1960, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1970, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1980, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:1990, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n",
      "epoch:2000, loss:0.00004565,loss_pde:0.00000253,loss_l2:4.31226569\n"
     ]
    }
   ],
   "execution_count": 112
  },
  {
   "id": "7cc2fa17c683c811",
   "cell_type": "code",
   "source": [
    "#预测\n",
    "#net2的泛化性\n",
    "u_up = to_numpy(u.flatten()[:, None]).max(0)\n",
    "u_lb = to_numpy(u.flatten()[:, None]).min(0)\n",
    "size = 301\n",
    "u_test = np.linspace(u_lb, u_up, size).reshape(-1, 1)\n",
    "f_exact = u_test*np.sqrt(1-u_test**2)\n",
    "u_test_train = torch.tensor(u_test, requires_grad=True, dtype=dtype).to(device)\n",
    "f_predict = to_numpy(model.dnn.forward(u_test_train))\n",
    "\n",
    "#泛化性\n",
    "plt.figure()\n",
    "plt.scatter(u_test, f_predict, label='f_predict', marker='s', facecolor='none', edgecolor='red')\n",
    "plt.plot(u_test, f_exact, label='f_exact', linewidth=3.0)\n",
    "plt.title('Net2_f_predict')\n",
    "plt.legend()\n",
    "plt.xlabel('u')\n",
    "plt.ylabel('f')\n",
    "plt.savefig(r\"Net2_f_predict_none_f.png\")\n",
    "plt.show()\n",
    "#f的error\n",
    "error_f = abs(f_predict-f_exact)\n",
    "plt.figure()\n",
    "plt.scatter(u_test, error_f, label='error_f', marker='o')\n",
    "#plt.plot(u_test, error_f2, label='f_exact', linewidth=3.0)\n",
    "plt.title('error_f_predict')\n",
    "plt.legend()\n",
    "plt.xlabel('u')\n",
    "plt.ylabel('f')\n",
    "plt.savefig(r\"error_f_predict_none_f.png\")\n",
    "plt.show()\n",
    "#log\n",
    "#MSE\n",
    "print('MSE error for every var')\n",
    "print('error_f is ',(error_f**2).mean())\n",
    "print('*****************************************')\n",
    "#L2 error\n",
    "print('L2 error for every var')\n",
    "print('error_f is ',np.sqrt((error_f**2).mean()))\n",
    "print('*****************************************')\n",
    "#相对误差\n",
    "print('relative error for every var')\n",
    "print('error_f is ',np.sqrt(np.linalg.norm(error_f, ord=2)/np.linalg.norm(f_exact, ord=2)))\n"
   ],
   "metadata": {
    "id": "7cc2fa17c683c811",
    "execution": {
     "iopub.status.busy": "2025-01-08T13:29:30.317026Z",
     "iopub.execute_input": "2025-01-08T13:29:30.317353Z",
     "iopub.status.idle": "2025-01-08T13:29:39.269335Z",
     "shell.execute_reply.started": "2025-01-08T13:29:30.317329Z",
     "shell.execute_reply": "2025-01-08T13:29:39.267479Z"
    },
    "trusted": true,
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "outputId": "c1f4fb36-3b5f-4f05-9e99-43e89196227d",
    "ExecuteTime": {
     "end_time": "2025-02-28T14:20:25.281469Z",
     "start_time": "2025-02-28T14:20:24.942494Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE error for every var\n",
      "error_f is  3.700420700762069e-05\n",
      "*****************************************\n",
      "L2 error for every var\n",
      "error_f is  0.00608310833436498\n",
      "*****************************************\n",
      "relative error for every var\n",
      "error_f is  0.12724260873710344\n"
     ]
    }
   ],
   "execution_count": 113
  },
  {
   "id": "c226b9d91185272e",
   "cell_type": "code",
   "source": "torch.save(model, 'Net2_none_f_model.pth')",
   "metadata": {
    "id": "c226b9d91185272e",
    "ExecuteTime": {
     "end_time": "2025-02-28T14:20:25.297041Z",
     "start_time": "2025-02-28T14:20:25.282471Z"
    }
   },
   "outputs": [],
   "execution_count": 114
  },
  {
   "cell_type": "code",
   "source": [],
   "metadata": {
    "id": "wcGkpz3Nc93E",
    "ExecuteTime": {
     "end_time": "2025-02-28T14:20:25.312196Z",
     "start_time": "2025-02-28T14:20:25.298043Z"
    }
   },
   "id": "wcGkpz3Nc93E",
   "outputs": [],
   "execution_count": 114
  }
 ]
}
